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Apply the Pythagorean Theorem

Apply the Pythagorean Theorem. Chapter 7.1. Sides of a Right Triangle. Hypotenuse – the side of a right triangle opposite the right angle and the longest side. Legs – the sides of a right triangle that are not the hypotenuse. Hypotenuse. Leg. Leg. The Pythagorean Theorem.

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Apply the Pythagorean Theorem

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  1. Apply the Pythagorean Theorem Chapter 7.1

  2. Sides of a Right Triangle • Hypotenuse – the side of a right triangle opposite the right angle and the longest side. • Legs – the sides of a right triangle that are not the hypotenuse. Hypotenuse Leg Leg

  3. The Pythagorean Theorem • In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the legs.

  4. Proving the Pythagorean Theorem • There are multiple ways of proving the Pythagorean Theorem. • If you can find a legitimate proof of the Pythagorean theorem you may earn 2 bonus points.

  5. Using the Pythagorean Theorem 6 8 x² 36 + 64 = x² 100= x²

  6. Find the missing leg x 3 5² x²+ 9 = 25 x² = 16

  7. Find the Area of the Triangle What is the formula for the area of a triangle? A = ½bh How will we find the height?

  8. Find the Area of the Triangle

  9. Pythagorean Triples • A Pythagorean Triple is a set of 3 positive integers or whole numbers that satisfies the Pythagorean theorem.

  10. Is it a Pythagorean Triple? yes • 3, 4, and 5 • 21, 28, and 35 • 30, 72, and 91 • 14, 48, and 50 yes no yes

  11. If I am given 2 sides of a right triangle where the sides are a Pythagorean triple, how do you find the 2 sides? There are 2 possible scenarios: • You are given both legs of the right triangle and need to solve for the hypotenuse. • You are given one leg and one hypotenuse and need to solve for the other leg.

  12. Given 2 sides: 20 and 25 • Scenario 2. • 20 and 25 are the leg and hypotenuse • 202 + x2 = 252 • 400 + x2 = 625 • x2 = 225 • X = 25 • This can be the answer for a Pythagorean triple because it is not a whole number. • Scenario 1. • 20 and 25 are the legs • 202 + 252 = x2 • 400 + 625 = x2 • 1025 = x2 • 32.02 = x • This cannot be the answer for a Pythagorean triple because it is not a whole number.

  13. Given 2 sides: 28 and 96

  14. Find the area when given a leg and the hypotenuse • Find the other leg by plugging the known values into the Pythagorean Theorem. • Use the 2 legs in the formula for area of a triangle • A = ½BH h b

  15. Find the area when given a leg and a hypotenuse. • L=8 and h= 16 • Aò+8ò=16ò • Aò+64=256 • Aò=192

  16. Find the area when given a leg and a hypotenuse. • L=13 and h= 17 • Aò+13ò=17ò • Aò+169=289 • Aò=120

  17. #3 – 7, 11- 16, 18 - 23

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